Question

The general value of $\theta$ satisfying both $sin\theta =\frac{-1}{2}$ and $tan\theta =\frac{1}{\sqrt{3}}$ is:

• A. $2n\pi$
• B. $2n\pi +7\pi /6$
• C. $n\pi +\pi /4$
• D. $2n\pi +\pi /4$

Answer 1

The correct option is B $2n\pi +7\pi /6$

Let us first find out $\theta$ lying between 0 and ${360}^o$.
Since $sin\theta =\frac{-1}{2}\Rightarrow \theta ={210}^o$ or ${330}^o$
and $tan\theta =\frac{1}{\sqrt{3}}\Rightarrow \theta ={30}^o$ or ${210}^o$
Hence $\theta ={210}^o$ of $\frac{7\pi }{6}$ is the value satisfying both.
$\therefore$ The general value of $\theta =(2n\pi +\frac{7\pi }{6}),nϵI$
Hence (B) is the correct answer.